代码随想录算法训练营第三十八天 动态规划

动态规划理论基础

牢记动态规划五部曲：
1.确定dp数组及其下标的含义
2.确定递推公式
3.dp数组如何初始化
4.确定遍历顺序
5.举例推导dp数组

509. 斐波那契数

class Solution {
public:
    int fib(int n) {
        if (n == 0) return 0;
        vector<int> dp(n + 1);
        dp[0] = 0;
        dp[1] = 1;
        for (int i = 2; i <= n; ++i) {
            dp[i] = dp[i - 1] + dp[i - 2];
        }
        return dp[n];
    }
};
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70. 爬楼梯

class Solution {
public:
    int climbStairs(int n) {
        if (n <= 2) return n;
        vector<int> dp(n + 1);
        dp[0] = 0;
        dp[1] = 1;
        dp[2] = 2;
        for (int i = 3; i <= n; ++i) {
            dp[i] = dp[i - 1] + dp[i - 2];
        }
        return dp[n];
    }
};
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746. 使用最小花费爬楼梯

class Solution {
public:
    int minCostClimbingStairs(vector<int>& cost) {
        int n = cost.size();
        vector<int> dp(n + 1);
        dp[0] = 0;
        dp[1] = 0;
        for (int i = 2; i <= cost.size(); ++i) {
            dp[i] = min(dp[i - 2] + cost[i - 2], dp[i - 1] + cost[i - 1]);
        }
        return dp[n];
    }
};
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